A Classification Theorem for Homotopy Commutative $H$-Spaces with Finitely Generated $/Bmod 2$ Cohomology Rings

Buch | Softcover

1991
American Mathematical Society (Verlag)
978-0-8218-2514-3 (ISBN)

Infos

Many homological properties of Lie groups are derived strictly from homotopy-theoretic considerations and do not depend on any geometric or analytic structure. An H-space is a topological space having a continuous multiplication with unit. Generalizing from Lie group theory, John Hubbuck proved that a connected, homotopy commutative H-space which is a finite cell complex has the homotopy type of a torus. There are many interesting examples of H-spaces which are not finite complexes - loop spaces are one example. The aim of this book is to prove a version of Hubbuck's theorem in which the condition that the H-space be a finite cell complex is replaced by the condition that it have a finitely-generated mod 2 cohomology ring. The conclusion of the theorem is slightly more general in this case, and some mild associativity hypotheses are required. The method of proof uses established techniques in H-space theory, as well as a new obstruction-theoretic approach to (Araki-Kudo-Dyer-Lashof) homology operations for iterated loop spaces.

Produkt-Details

• Erscheint lt. Verlag: 30.8.1991
• Reihe/Serie: Memoirs of the American Mathematical Society
• Verlagsort: Providence
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: Memoirs of the AMS; No. 449
• ISBN-10: 0-8218-2514-3 / 0821825143
• ISBN-13: 978-0-8218-2514-3 / 9780821825143
• Zustand: Neuware